Hairdressing appliances for straightening, curling, or crimping hair typically comprise a portable treatment unit composed in particular of two arms, or jaws, which each have a surface that can be flat or curved, the two arms being hinge-connected to one another to form a clamp configured for clamping hair between the two surfaces facing one another as the two arms are brought together. These two arms also comprise a gripping zone enabling the opening and closing of the clamp and the handling thereof during the styling. At least one of these two surfaces has a heating device enabling the treatment of hair with heat while it is clamped between the two surfaces. The straightening of a lock of hair is effected by clamping the lock of hair between the two surfaces and by moving the closed clamp along this lock of hair, from the root to the tip. The curling of a lock of hair is effected by clamping the lock of hair between the two surfaces and by winding, at least partially, this lock of hair around the surfaces, the heat making it possible to set the curl. For improving the hair styling, it is possible to use a steam treatment as a supplement to the heat treatment, said steam being applied to the hair.
To this end, the Applicant has already developed a steam hairdressing appliance, which is described in the patent application published under the number FR 2 967 017 A1. Besides the aforementioned technical features, the hairdressing appliance according to FR 2 967 017 A1 comprises a base remote from the portable treatment unit, said portable treatment unit composed of a clamp as described above. The base comprises a water tank and a water pump which, when turned on, pumps the water in the tank for supplying the clamp. One of the arms of the portable treatment unit comprises a vaporization chamber equipped with a heating device. Once the hairdressing appliance has attained its optimum operating conditions and when the user wishes to use steam for styling his/her hair, the pump injects water into the vaporization chamber; this water vaporizes under the action of the heating device, and the steam is then applied to the hair. Thus the clamp makes it possible to treat hair with heat and with steam. In the hairdressing appliance described in FR 2 967 017 A1, connection means between the base and the portable treatment unit make it possible to supply said treatment unit with electricity and water from the base. The portable treatment unit further comprises a circuit board for controlling the heat and steam treatment system and the pump, this control circuit board being located in the portable treatment unit.